Do Regulatory quality and Researchers go together across countries?

Across 131 countries the link before adjusting for anything is r = +0.77, on a scale from -1 (opposite) to +1 (in step). A version that uses only each country's rank gives +0.77.

Does the link hold within countries over time, not just across countries?

Comparing each country only with itself across 1996-2024, and setting aside what happened worldwide in each year, the link is -0.017 (101 countries, 1,721 country-years). Using year-to-year changes, it is +0.002.

Does Regulatory quality cause Researchers?

This analysis cannot answer that. It shows only that the two go together. A link between two country measures, adjusted or not, does not show that either one changes the other. Country figures also say nothing about individual people.

Regulatory quality vs. Researchers

Holds up after adjusting for income

Across 131 countries, Regulatory quality and Researchers rise and fall together at r = +0.77 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to +0.52 (q = 0.0094, allowing for the many pairs tested). Much of the first figure is that both measures rise with national income, but a moderate positive link remains. Caution: direction is not consistent across regions.

Comparing countries across the middle half of researchers, 139 to 3,181 per million people, regulatory quality is better by 0.859 points at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 0.478 points.

Link before adjusting (r)+0.775p = 1.8e-27 · 131 countries

After adjusting for national income+0.520p = 2.3e-10 · likely range [+0.38, +0.64]

p, allowing for regions0.003standard error 0.106 · 7 regions

Check for luck (q)0.009across 12,497 pairs

How to read these.r runs from −1 (one goes up as the other goes down) to +1 (they rise together), and 0 means no link. Adjusting for national income means comparing countries with the same GDP per person, so differences in wealth can’t explain the link. Income is used in percentage terms, since an extra $1,000 means more to a poor country than to a rich one. p is how likely a link this strong would be if there were really none. Below 0.05 means it is unlikely to be chance. Very small values are written in short form: 1.1e-32 means a decimal point followed by 31 zeros and then 11, so very close to zero. The likely range is where the true figure probably lies, and a range that crosses zero means the link could easily be chance. Countries in the same region tend to resemble each other, so the third figure allows for that, which gives a fairer p. The standard error is the typical size of the error in r. Finally, testing this many pairs means some will look strong by luck alone. A q below 0.05 means this link is unlikely to be one of those.

Regulatory quality · index (approx. -2.5 to 2.5)link with income +0.83 · proxy

Researchers · per million peoplelink with income +0.85 · proxy

Both of these rise and fall closely with national income, so a strong link between them before adjusting was close to certain. Read the adjusted figure, not the first one.

“Link with income” is how closely each measure tracks GDP per person across countries, from −1 to +1.

Every country as a dot

best-fit line line after adjusting

Four ways to measure the link

Method	r	p	Countries
Standard (Pearson), not adjusted	+0.775	1.8e-27	131
By rank (Spearman), not adjusted	+0.769	7.1e-27	131
Standard (Pearson), adjusted for national income	+0.520	2.3e-10	131
By rank (Spearman), adjusted for national income	+0.139	0.114	131

The rank version uses only each country’s place in line, from lowest to highest, so a few extreme countries count for less. The adjusted and unadjusted versions use the same 131 countries: those that report both measures and GDP per person. So the gap between them comes from the adjustment, not from a change in which countries are counted. Drop in the size of r after adjusting: +0.255 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from +0.499 (without FIN) to +0.546 (without IRN). The bar above shows that range on a scale from −1 to +1, with the solid line at the full result. The single country that moves r most: IRN (+0.026).

Fragile: this link may not hold up.

direction is not consistent across regions

Within each region

Countries are not separate, unrelated cases, and neighbors share a lot. A link that holds inside each region is far more believable than one that shows up only when comparing regions.

	n	r
East Asia & Pacific	18	+0.42
Europe & Central Asia	45	+0.50
Latin America & Caribbean	17	-0.08
Middle East, North Africa, Afghanistan & Pakistan	17	-0.18
Sub-Saharan Africa	29	+0.41

By income third

If the link shows up only in the richest third of countries, it is a feature of rich countries, not a general pattern.

	n	r
Poorest third	44	+0.21
Middle third	43	-0.23
Richest third	44	+0.62

By largest religious group

Countries grouped by a label they share, such as main religion, rather than by a number. Groups of fewer than twelve countries are not shown. These groups differ in income, region and history all at once. So a gap between them is a place to start asking questions, not an answer.

	n	r
Christians	80	+0.61
Muslims	32	-0.25

By last european coloniser

	n	r
France	13	+0.23
Never a European colony	15	+0.23
Spain	16	+0.22
United Kingdom	36	+0.60

Without outliers (countries far outside the middle half of countries on either measure, by more than one and a half times the width of that middle half): r = +0.471 after dropping 5 countries.

Two series, one country

Both measures over the years for one country you pick. The two charts are stacked so they share only the years along the bottom.

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Over time, within countries

Everything above compares countries with each other at one moment. This section compares each country only with itself over 29years. So a link here can’t come from anything about a country that stays the same, such as its history, geography, institutions or culture.

Within countries over time, there is no link that is clearly more than chance (r = -0.017, comparing each country only with itself over the years, and each year only with the same year elsewhere). Whatever the cross-country picture shows, countries whose regulatory quality moved did not tend to see their researchers move with it.

Across countries (adjusted)+0.520for comparison

Within countries+0.043each country vs itself

…and vs the same year elsewhere-0.017q = 0.908 · 101 countries

Year-on-year changes+0.002q = 0.977

Read with care.

Almost all of the second indicator's variation is between countries, so the within-country estimate rests on a small part of the data.

1,721 country-years (one country in one year), 101 countries, 1996–2024, about 17 years each on average. Share of the variation that happens within countries over time: 12% for Regulatory quality, 5% for Researchers. The margins of error allow for each country appearing many times, and for each year’s value being close to the year before.

Year-to-year changes are a cautious test, not a final answer. Looking only at changes from one year to the next removes each country’s own trends. But it also makes measurement mistakes louder, which pulls the results toward zero. A near-zero result here is weak evidence of no link, not proof.

With one measure years behind the other

Same year (lag 0): -0.017. A peak away from zero does not show which comes first. These series change slowly — this year’s value is close to last year’s. That makes the curve smooth and nearly symmetric, whatever produced the data. Even a sharp peak at one lag (a gap of some years) would not prove that one measure changes the other.

The largest value on this curve (-0.09 at lag -4) is higher than the same-year one by 0.07. That gap is not a finding. It is the largest of 21 closely related estimates, and picking the biggest of many tests always makes it look bigger. That is exactly why nothing on this site is ranked or chosen by lag.

The data

	index (approx. -2.5 to 2.5)	per million people	Years
Singapore SGP	2.13	8,782	2024, 2022
Finland FIN	1.96	8,315	2024, 2023
Denmark DNK	1.93	8,838	2024, 2023
New Zealand NZL	1.84	5,435	2024, 2023
Luxembourg LUX	1.84	5,359	2024, 2023
Ireland IRL	1.79	5,753	2024, 2023
Switzerland CHE	1.77	6,108	2024, 2023
Hong Kong SAR, China HKG	1.74	5,874	2024
Australia AUS	1.72	4,569	2024, 2010
Netherlands NLD	1.72	6,563	2024, 2023
Sweden SWE	1.67	8,911	2024, 2023
Norway NOR	1.67	7,451	2024, 2023
United Kingdom GBR	1.51	4,473	2024, 2017
Germany DEU	1.5	5,926	2024, 2023
Estonia EST	1.4	4,800	2024, 2023

Kaufmann, D. and A. Kraay, Worldwide Governance Indicators, World Bank
World Bank, World Development Indicators

Sources

Regulatory quality

Regulatory Quality (estimate)

World Bank · CC BY 4.0 · updated annual

Researchers

Researchers in R&D (per million people)

UNESCO Institute for Statistics · CC BY 4.0 · updated quarterly

Researchers counted as full-time equivalents (two half-time researchers count as one), from national research surveys that many countries run only now and then. So coverage is thin outside the OECD.

How this was computed

Data used: most recent value in 2010-2025; values come from 2010–2024. To adjust for income, each measure is first predicted from GDP per person (in percentage terms, on a log scale) with a straight-line fit. Only what is left over is then compared. This is called a partial correlation. The line is drawn the standard way (ordinary least squares), which picks the line that comes closest to all the countries at once. The error margins allow for countries in the same region resembling each other, using 7 World Bank regions. The q-value corrects for testing all 12,497 pairs at once, using the Benjamini–Hochberg method. Underlying data last updated DYB 2024. How the country data works · explore Regulatory quality and Researchers

This page shows that two measures go together. It does not show that Regulatory quality changes Researchers, or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.